Ministers have been accused of attempting to reintroduce controversial plans to reduce staff-to-child ratios for childcare in England by quietly launching a survey of parents asking if they are happy with staffing levels.

Childcare pressure groups and Labour said that the online poll, promoted by the department for education on Facebook and Twitter, was a back-door manoeuvre which could be easily manipulated by civil servants.

They claim that the questions have been phrased in a way so that the findings could be manipulated to create an unrealistic interpretation of parents' opinions.

It comes as education secretary Michael Gove prepares to debate the government's decision to allow unqualified teachers to teach in free schools with his new opposite number, Tristram Hunt.

The Pre-School Learning Alliance said the survey was biased and unscientific. Its chief executive, Neil Leitch, said: "We are extremely concerned that once again the government appears to be using ratio changes as a money-saving measure – and, what's more, that they have deemed it appropriate to collect evidence on this issue through such an unbalanced, biased survey.

"Anyone who has read the survey will have seen that the way the questions are phrased is likely to allow for a misleading interpretation of the findings."

Lucy Powell, the shadow childcare minister, said: "It looks like David Cameron may be trying to pull a fast one on parents, resurrecting their worrying plan to increase the number of children childminders and nursery staff can look after. This issue was dead in the water after parents, providers and experts raised serious concerns that these changes risk child safety and will not reduce costs to parents."

The survey, entitled "Ratios in nurseries and other childcare settings", asks 10 questions of parents who have a three- or four-year-old at nursery, all of which relate to staffing levels and teaching qualifications.

Questions include "Do you know how many members of staff there should be for the number of children in your child's nursery? If yes, what is the ratio? If no, what do you think it should be?"

It asks multiple choice questions including "Do you look to the nursery's Ofsted report? Which aspects in particular concern you?" and offers six possible answers including "safety" "what the children learn" and "the ratio of staff to children".

This summer, the government scrapped plans to reduce staff-to-child ratios in nursery settings after fierce criticism from the sector.

In June, the Conservative children's minister, Liz Truss, was forced to drop the plans after an intervention by Nick Clegg, the deputy prime minister.

An extensive consultation had shown that her two key aims would fail, Clegg said. Cutting staff-to-child ratios would not necessarily drive down the costs of childcare – and might even increase them – and would not necessarily improve standards, he said.

Any future move will be fought by Clegg. A senior Liberal Democrat source said: "There is no prospect of the coalition government revisiting the issue of childcare ratios. Nick Clegg made very clear they cannot proceed. The issue has been put to bed and will not get up."

Under the changes put forward earlier this year, ratios for two-year-olds would have changed from four children per adult to six, and ratios for ones and under from three children per adult to four.

The option for providers to have a 1:13 ratio for three- and four-year-olds has been available since 2008. The DfE has also been criticised for limiting the reach of the survey by using social media sites Facebook and Twitter to receive responses instead of publishing it on the department's own website.

The Professional Association for Childcare and Early Years (Pacey) has also criticised the survey and questioned the usefulness of any information gained from feedback. Liz Bayram, chief executive of Pacey, said: "Pacey is concerned to hear that the Department for Education is consulting parents on childcare ratios, given that there was widespread criticism of the department the last time it proposed this reform.

"We also question how this crude approach to gaining parent feedback is going to provide the DfE with any meaningful information."

A DfE source said that the survey was part of a fact-finding exercise which hoped to be able to examine the attitude of private nursery users – but the source struggled to explain why the survey does not ask parents to say whether their children are cared for in private or public nurseries. A spokeswoman said: "In 2008 ratios were relaxed so nurseries could have classes of up to 13 children aged three or over when led by a teacher. School nurseries take advantage of this flexibility, whereas private nurseries are less likely to do so.

"We have always said we want this flexibility to be used more widely – because evidence shows that teacher-led provision improves outcomes for children – and it is important that we explore what barriers are preventing nurseries from doing this."